RVLUmin::LBFGSOp< Scalar > Class Template Reference

LMBFGSOp implements the limited memory BFGS approximation to the inverse Hessian of a twice-differentiable function. More...

#include <lbfgsalg.hh>

Inheritance diagram for RVLUmin::LBFGSOp< Scalar >:

List of all members.


Public Member Functions
	LBFGSOp (const Space< Scalar > &_sp, Scalar ihs, int maxnum)
	Usual constructor.
	LBFGSOp (const LBFGSOp< Scalar > &op)
	Copy constructor.
	~LBFGSOp ()
const Space< Scalar > &	getDomain () const
const Space< Scalar > &	getRange () const
Scalar	getScale ()
void	update (const Vector< Scalar > &x, const Vector< Scalar > &xnext, const Vector< Scalar > &g, const Vector< Scalar > &gnext)
	update requires current and next $x$ and current and next gradient.
void	reset ()
ostream &	write (ostream &str) const
	write methods to print out useful information about the object.
Protected Member Functions
LinearOp< Scalar > *	clone () const
void	apply (const Vector< Scalar > &x, Vector< Scalar > &y) const
void	applyAdj (const Vector< Scalar > &y, Vector< Scalar > &x) const

Detailed Description

template<class Scalar>
class RVLUmin::LBFGSOp< Scalar >

LMBFGSOp implements the limited memory BFGS approximation to the inverse Hessian of a twice-differentiable function.

This approximation uses local changes to the gradient to gradually build up an estimate of the Hessian for use in nonlinear optimization problems.

For details of the algorithm, see the paper

"Updating Quasi-Newton Matrices with Limited Storage" by Jorge Nocedal, Math. of Computation, Vol. 35, no. 151, p.p. 773--782.

Note that the operator is an approximation to the inverse Hessian, so the the apply method computes the quasi-Newton step.

The BFGS approximation is based on successive rank-one perturbations to an initial approximation; these rank-one perturbations can be represented as outer products. This class allows the user to provide a symmetric positive definite operator to define an alternate inner product, which then changes the definition of the outer product. In the context of an optimization problem, this is equivalent to implementing the algorithm in the alternate inner product.

Definition at line 72 of file lbfgsalg.hh.

Constructor & Destructor Documentation

template<class Scalar>

RVLUmin::LBFGSOp< Scalar >::LBFGSOp	(	const Space< Scalar > &	_sp,
		Scalar	ihs,
		int	maxnum
	)

Usual constructor.

Needs a multiple of the identity to use for the initial inverse Hessian approximation, the maximum number of updates, and, optionally, an operator to change the inner product.

Definition at line 161 of file lbfgsalg.hh.

template<class Scalar>

RVLUmin::LBFGSOp< Scalar >::LBFGSOp ( const LBFGSOp< Scalar > & op )

Copy constructor.

Definition at line 169 of file lbfgsalg.hh.

References RVLUmin::LBFGSOp< Scalar >::Svec, and RVLUmin::LBFGSOp< Scalar >::Yvec.

template<class Scalar>

RVLUmin::LBFGSOp< Scalar >::~LBFGSOp ( )

Definition at line 178 of file lbfgsalg.hh.

Member Function Documentation

template<class Scalar>

LinearOp<Scalar>* RVLUmin::LBFGSOp< Scalar >::clone ( ) const [protected, virtual]

Implements RVL::Operator< Scalar >.

Definition at line 93 of file lbfgsalg.hh.

template<class Scalar>

void RVLUmin::LBFGSOp< Scalar >::apply	(	const Vector< Scalar > &	x,
		Vector< Scalar > &	y
	)			const `[protected, virtual]`

Implements RVL::Operator< Scalar >.

Definition at line 98 of file lbfgsalg.hh.

References RVL::Vector< Scalar >::copy(), and RVL::Vector< Scalar >::scale().

template<class Scalar>

void RVLUmin::LBFGSOp< Scalar >::applyAdj	(	const Vector< Scalar > &	y,
		Vector< Scalar > &	x
	)			const `[protected, virtual]`

Implements RVL::LinearOp< Scalar >.

Definition at line 144 of file lbfgsalg.hh.

References RVL::LinearOp< Scalar >::applyOp().

template<class Scalar>

const Space<Scalar>& RVLUmin::LBFGSOp< Scalar >::getDomain ( ) const [virtual]

Implements RVL::Operator< Scalar >.

Definition at line 180 of file lbfgsalg.hh.

template<class Scalar>

const Space<Scalar>& RVLUmin::LBFGSOp< Scalar >::getRange ( ) const [virtual]

Implements RVL::Operator< Scalar >.

Definition at line 181 of file lbfgsalg.hh.

template<class Scalar>

Scalar RVLUmin::LBFGSOp< Scalar >::getScale ( )

Definition at line 184 of file lbfgsalg.hh.

template<class Scalar>

void RVLUmin::LBFGSOp< Scalar >::update	(	const Vector< Scalar > &	x,
		const Vector< Scalar > &	xnext,
		const Vector< Scalar > &	g,
		const Vector< Scalar > &	gnext
	)